Since there are a lot of world problems, choosing one world problem is quite difficult. = Correct.
Explanation: Sentence is clear and natural.

Including Gender difference, war, rape and etc, they are all serious world problems. = Including gender differences, war, rape, and so on, they are all serious world problems.
Explanation: “Gender difference” = “gender differences”; “and etc” = “and so on” (redundant otherwise); added commas for clarity.

But I would want to solve the 'war' problem. = But I would want to solve the problem of war.
Explanation: More natural phrasing.

From the past to the future, war happened because of the greedy interests. = From the past to the present, wars have happened because of greedy interests.
Explanation: “to the future” = “to the present” (talking historically); “war happened” = “wars have happened” (plural + present perfect for ongoing relevance); removed “the” before “greedy interests.”

Owing to those some greedy national interests, many innocent citizens sacrificed. = Because of some greedy national interests, many innocent citizens were sacrificed.
Explanation: “Owing to those some” = “Because of some” (natural); “sacrificed” = “were sacrificed” (passive voice fits context).

War destroy their towns, families, and also a normal life. = War destroys towns, families, and normal life.
Explanation: “destroy” = “destroys” (present tense, singular subject); “their” = removed for general statement; simplified “and also a normal life” = “and normal life.”

Good job! Your ideas are strong and meaningful. Keep it up!